Slice eggs in half lengthwise and carefully remove the yolks. Arrange egg whites on a serving plate. Set aside.
In a food processor, add egg yolks, mayonnaise, mustard, hot sauce, cajun seasoning, and salt. Pulse until mixture is smooth and creamy. (Alternatively, mash yolks in a bowl with a fork, then add remaining ingredients and stir until smooth.) Taste and add more hot sauce as desired.
Pipe filling evenly between eggs and top with green onions and (optionally) more cajun seasoning.
Refrigerate eggs, covered, until ready to serve. Deviled eggs can sit out for two hours before needing additional refrigeration.
Notes
Storage: Deviled eggs will keep for 3 to 4 days in the refrigerator. They can sit out for up to two hours before leftovers must be refrigerated or discarded.
Make ahead: Deviled eggs can be made a day or two ahead and stored in the refrigerator until ready to serve.
Cajun seasoning: If your cajun seasoning includes salt, omit the salt listed in the recipe.